Spectral efficiency and data throughput are key requirements that a scheduler needs to address within an 802.16m system implementation. To maximize spectral efficiency and data throughput a base station (BS) scheduler must optimally allocate OFDMA subcarriers or subchannels to users within its cell. Assuming NFFT denotes an IFFT/FFT length and Nused<NFFT the number of used subcarriers, SNused denotes a set that contains the integer-valued subcarrier indices of the Nused subcarriers, and the integer-valued variable 1≦nUsers≦Nused denotes the number of users to be serviced by the nth DL or UL subframe, for nUsers users a scheduler specified subcarrier allocation for the nth subframe may be denoted as:A[n]={A0[n],A1[n], . . . ,AnUsers−1[n]}.  (1)Allocation set A[n] contains distinct subcarrier subsets A0[n], A1[n], . . . , AnUsers−1[n] which are disjoint subsets of SNused. The ith subcarrier subset Ai[n] consists of Ni subcarriers. Depending on channel conditions, subcarriers within each Ai[n] may be contiguous or non-contiguous. If all Nused subcarriers are used the equality:N0+N1+ . . . +NnUsers−1=Nused  (2)must be true for a specified allocation A[n].In general, the BS may specify a subcarrier allocation A[n] by deterministically or pseudo-randomly permuting the elements of the subcarrier set SNused and then partitioning the resulting permutation set into subcarrier subsets Ai[n], i=0, 1, . . . , nUsers−1. For example, the elements in set S16={0, 1, 2, . . . , 15} may be pseudo-randomly permuted giving the permuted set:S16Perm={0,5,7,9,10,12,14,2,3,4,11,13,6,8,15}  (3)This set can then be partitioned to produce the subcarrier subsets:A0[n]={0,5}A1[n]={7,9,10,12,14}A2[n]={2,3,4,11,13}A3[n]={6,8,15}  (4)The multinomial coefficient:
                              C          ⁡                      (                                          N                0                            ,                              N                1                            ,              …              ⁢                                                          ,                              N                                                      n                    Users                                    -                  1                                                      )                          =                                            N              used                        !                                                              N                0                            !                        ⁢                                          N                1                            !                        ⁢                                                  ⁢            …            ⁢                                                  ⁢                                          N                                                      n                    Users                                    -                  1                                            !                                                          (        5        )            equals the number of ways the scheduler may allocate Nused subcarriers to nUsers users with N0 subcarriers in the first subset A0[n], N1 subcarriers in the second subset A1[n], and so on. It is clear that finding an optimal allocation from all possible C(N0, N1, . . . , NnUsers−1) subcarriers combinations is not a practical task for a BS scheduler. For example, the multinomial coefficient for the simple example above is:
                              C          ⁡                      (                                          N                0                            ,                              N                1                            ,                              N                2                            ,                              N                3                                      )                          =                                            16              !                                                      2                !                            ⁢                              5                !                            ⁢                              5                !                            ⁢                              3                !                                              =                      7.2649            ×                          10              9                                                          (        6        )            
Indeed, the problem of multi-user subcarrier/subchannel allocation by a BS can be computationally complex and time consuming, especially when the number of subcarrier/subchannel is large. In addition, the amount of overhead for signaling subcarrier/subchannel allocations and uplink channel quality reporting for user may substantially degrade spectral efficiency gains associated with multi-user diversity. Implementation difficulties may also arise. For example, a receiving BS will need to support numerous frequency offsets and dynamic ranges. Thus, an improved physical layer resource unit is required to simplify a BS's scheduling task and to help minimize associated overhead and signaling.